Great Britain's men's quadruple sculls crew came fifth in the opening rowing race of Friday's finals session.
Germany took the gold with Croatia in silver and Australia won the bronze.
.The Germans set the pace for the length of the final and then accelerated clear of the Croatians, who had been unbeaten in 2012 up until the Olympic final.
Australia's world champions finished with bronze as Britain's medal bid faltered over the second 1,000 metres after a strong start.
Stephen Rowbotham, Charles Cousins, Tom Solesbury and Matt Wells were third at the halfway stage, having had to battle through the worst of the water in blustery conditions at Eton Dorney.
Despite missing out on the podium, they could be proud of their achievement after becoming the first British men's quad to qualify for an Olympic final.
And trailing behind them in sixth were the reigning Olympic champions from Poland.